Maximilian Ganster

Locally closed sets and LC-continuous functions

In this paper we introduce and study three different notions of generalized continuity, namely LC-irresoluteness, LC-continuity and sub-LC-continuity. All three notions are defined by using the concept of a locally closed set. A subset S of a topological space X is locally closed if it is the intersection of an open and a closed set. We discuss some properties of these functions and show that a function between topological spaces is continuous if and only if it is sub-LC-continuous and nearly continuous in the sense of Ptak. Several examples are provided to illustrate the behavior of these new classes of functions.

ON p-CLOSED SPACES

We will continue the study of p-closed spaces. This class of spaces is strictly placed between the class of strongly compact spaces and the class of quasi-H-closed spaces. We will provide new characterizations of p-closed spaces and investigate their relationships with some other classes of topological spaces.

On generalized closed sets

Abstract In this paper we study generalized closed sets in the sense of N. Levine. We will consider the question of when some classes of generalized closed sets coincide. Also, some lower separation axioms weaker than T1 are investigated. We will provide characterizations of extremally disconnected spaces and sg-submaximal spaces by using various kinds of generalized closed sets.

On pre-Λ-Sets and pre-v-Sets

We introduce the notions of a pre-Λ-set and a pre-V-set in a topological space. We study the fundamental properties of pre-Λ-sets and pre-V-sets and investigate the topologies defined by these families of sets.

On semi-g-regular and semi-g-normal spaces ⁄

The aim of this paper is to introduce and study two new classes of spaces, called semi-g-regular and semi-g-normal spaces. Semi-g-regularity and semi-g-normality are separation properties obtained by utilizing semi-generalized closed sets. Recall that a subset A of a topological space (X;?) is called semi-generalized closed, briefly sg-closed, if the semi-closure of A µ X is a subset of U µ X whenever A is a subset of U and U is semi-open in (X;?) .

On pairwise paracompactness

This paper answers a recent question concerning the relationship between two notions of paracompactness for bitopological spaces. Romaguera and Marin defined pairwise paracompactness in terms of pair open covers, motivated by a characterization of paracompactness due to Junnila. On the other hand, Raghavan and Reilly defined a bitopological space ( X , τ, σ) to be δ-pairwise paracompact if and only if every τ open (σ open) cover of X admits a τ V σ open refinement which is τ V σ locally finite. It is shown that pairwise paracompactness implies δ-pairwise paracompactness, and that the converse is false.

On Compactness with Respect to Countable Extensions of Ideals and the Generalized Banach Category Theorem

We extend a theorem of Hamlett and Janković by proving that if a topological space (X, τ) is compact with respect to the countable extension of I, then the local function A*(I) of every subset A of X with respect to τ and I is a compact subspace with respect to the extension Ĩ in A* (I). We also give a generalized version of the Banach category theorem.

Recent Progress in the Theory of Generalized Closed Sets

In this paper we present an overview of our research in the field of generalized closed sets (in the sense of N. Levine). We will demonstrate that certain key concepts play a decisive role in the study of the various generalizations of closed sets.

ON LOCALLY COUNTABLY S-CLOSED AND LOCALLY RC-LINDELÖF SPACES

Abstract The aim of this paper is to continue the study of some topological properties weaker than S-closed, this time via a local point of view. We show that every focally countably S-closed km-perfect space is extremally disconnected as well as that every locally rc-Lindelof mildly Hausdorff space is δ-extremally disconnected.